1. PPT11: Advanced Surface Construction Techniques
CAP 6736
Geometric Modeling
PPT11: Advanced Surface Construction Techniques
PPT and video are due no later than April 5
Submit to:
This template file is just an outline of the presentation
that you need to complete. Additional pages may
be necessary to fully explore the topic above.
Each page should contain adequate text as well
as illustrations. You are free to use all publicly
available information (text as well as graphics) as long as
the sources are properly acknowledged.

2. Team members’ contributions
Member [name]:

3. Part I: Technical details
For this part you will need an equation editor. You may use:
MS equation editor,
MathType,
LaTeX, or
Handwritten equations if all else fails

4. Swung Surfaces Suggested content: swung surfaces
profile and trajectory curves
surface construction

5. Swung Surfaces
Suggested content:
swung surfaces
surface examples

6. Skinned Surfaces Suggested content: skinned surfaces
cross-sectional curve examples

7. Skinned Surfaces Suggested content: skinned surfaces
making curves compatible
common knot vector

8. Skinned Surfaces Suggested content: skinned surfaces
surface construction via interpolation

9. Skinned Surfaces Suggested content: skinned surfaces
parameters and knots

10. Skinned Surfaces Suggested content: skinned surfaces
skinning using a guide curve

11. Skinned Surfaces Suggested content: skinned surfaces
skinning using a guide curve and derivatives

12. Skinned Surfaces Suggested content: skinned surfaces with spine curve
examples

13. Skinned Surfaces Suggested content: skinned surfaces with spine curve
examples

14. Skinned Surfaces Suggested content: skinned surfaces with spine curve
section curve positioning

15. Skinned Surfaces Suggested content: skinned surface issues
rational cross-sectional curves give rise to negative weights

16. Skinned Surface Revisited
Suggested content:
skinned surface
skinning in practice

17. Skinned Surface Revisited
Causes of lofting problems:
Parametrization inconsistencies: parameters must flow the same way along each section curve
Positioning inconsistencies: section curves must be placed with care or wiggles or even self intersections may occur
Continuity inconsistencies: rational curves must be parametric continuous in homogeneous space not just in Euclidean space
Weight problems: large weight changes may cause negative weights during interpolation and weight scaling may produce nonsensical surfaces

18. Skinned Surface Revisited
Suggested content:
skinned surface
skinning to approximate cross-sectional curves
Remove bad parametrization and weight problems

19. Skinned Surface Revisited
Suggested content:
skinned surface
examples

20. Skinned Surface Revisited
Suggested content:
skinned surface
examples

21. Swept Surfaces Suggested content: swept surfaces
trajectory and section curves
translational sweep

22. Swept Surfaces
Suggested content:
swept surfaces
example

23. Swept Surfaces Suggested content: swept surfaces
trajectory and section curves
non-translational sweep
surface construction

24. Swept Surfaces Suggested content: swept surfaces no trajectory control

25. Swept Surfaces Suggested content: swept surfaces no scaling
scaling of section curves

26. Swept Surfaces Suggested content: swept surfaces no trajectory control

27. Swept Surfaces Suggested content: swept surface problems
self intersection
wavy surfaces

28. Swept Surfaces Suggested content: swept surface problems
incorrect curve placement causes flipped surfaces

29. Swept Surfaces Suggested content: swept surface problems
better curve placement with a local moving frame

30. Gordon Surfaces Suggested content: Gordon surfaces
bi-directional curve network
compatibility conditions
blending functions
construction of Gordon surface

31. Gordon Surfaces Suggested content: Gordon surfaces
construction of Gordon surface
u-directional lofting

32. Gordon Surfaces Suggested content: Gordon surfaces
construction of Gordon surface
v-directional lofting

33. Gordon Surfaces Suggested content: Gordon surfaces
construction of Gordon surface
interpolation through intersection points

34. Gordon Surfaces Suggested content: Gordon surfaces
construction of Gordon surface from three surfaces

35. Coons Surfaces Suggested content: Coons surfaces
bi-linearly blended patch to four boundaries

36. Coons Surfaces Suggested content: Coons surface construction
ruled surfaces in both directions

37. Coons Surfaces Suggested content: Coons surface construction
bi-linear surface and Coons patch

38. Coons Surfaces Suggested content: bi-cubically blended Coons surface
boundary curves, cross-derivatives and twist vectors
surface control points

39. Coons Surfaces Suggested content: bi-cubically blended Coons surface
cubic blend in one direction

40. Coons Surfaces Suggested content: bi-cubically blended Coons surface
cubic blend in another direction

41. Coons Surfaces Suggested content: bi-cubically blended Coons surface
bicubic tensor product surface

42. Coons Surfaces
Suggested content:
bi-cubically blended Coons surface

43. Part II: Design examples

44. Design Examples Suggested content:
Add design examples: images and/or videos
Give credit to the designers

45. Part III: GM lab
For this part of the assignment you may use an existing system,
such as Blender, or write the code and visualize the result
using graphics tools like Processing.

46. Geometric Modeling Lab
Suggested project:
Design shapes using advanced surface construction